Curvature properties of projective semi-symmetric linear connections

Milan Lj. Zlatanović; Miloš Z. Petrović; Miroslav D. Maksimović;


We study a projective semi-symmetric linear connection on a differentiable manifold $\mathcal{M}$ endowed with a Riemannian metric $g$. We start with linearly independent curvature tensors $\underset\theta R$, $\theta=0,1,\ldots,5$ and derive the tensors $\underset\theta W$ for $\theta=0,1,\ldots,5$ that, as we show, coincide with the Weyl tensor of projective curvature $W{}^g$. This confirms the well-known fact that there does not exist a generalization of the Weyl projective curvature tensor $W{}^g$.

Vol. 24 (2023), No. 3, pp. 1615-1635
DOI: 10.18514/MMN.2023.4225

Download: MMN-4225